In regards to the sinner's prayer, saying a sinner's prayer will not accomplish anything on its own. I must have prayed the sinner's prayer 20 different times with Pat Robertson while watching the 700 Club when I was a teenager, yet nothing happened. Why? Because there was no repentance and faith. Such a prayer needs to include what a person knows, understands, and believes about their sinfulness and need for salvation, followed by repentance/faith.
For a person who comes to the realization that he is lost and in need of Jesus Christ to save him, he may only obtain salvation by grace through faith in Jesus Christ alone. He needs to understand that Jesus Christ, God in human form, took his sins and paid the penalty for his sins by His sacrifice on the cross of Calvary, was buried, and rose again the third day, and he need only make a genuine and willful decision to totally trust in Jesus and His payment for his sin in order to receive eternal life. In doing this one is calling on the name of the Lord to save him.
Now if subsequent to such a decision, the person would like to pray what some call a "sinner’s prayer," (calling on the name of the Lord to save him in prayer) he may do so, as long as he understands that it was his decision to trust in Christ for salvation that apprehends his salvation and not simply reciting a prayer in of itself. Reciting a prayer, in of itself does not save, as if it's a magical formula to recite a set of words, but prayer may be used to call upon the name of the Lord.